Law-enforcement officials on Monday responded to the escalating gun violence on Seattle streets by promising to prosecute more gun-carrying criminals under federal firearms statutes, which carry longer prison terms than are available under current state law.

U.S. Attorney Jenny Durkan said that, until now, only the “worst of the worst” gun-carrying felons would be referred to a special cross-designated prosecutor who would decide if they were eligible for charges under federal “felon in possession of a firearm” statutes that carry prison sentences of up to 10 years. Durkan said Monday that she has removed that caveat and now, anyone eligible for federal prosecution and more prison time will get it.

“We are here today to send a clear message: If you bring a gun to a crime, you will do more time. And most likely, it will be federal time,” Durkan said during a news conference at the King County Prosecuting Attorney’s Office in Seattle.

Durkan, flanked by King County Prosecutor Dan Satterberg, Seattle Mayor Mike McGinn and law-enforcement officials, said prosecution is only one remedy for a tangled problem with deep roots in the social fabric. For example, dealing with access to firearms by the mentally ill and youngsters will require solutions outside the criminal-justice system, she said.

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But that’s not why McGinn, Durkan and other law-enforcement luminaries gathered Monday. Their piece of the puzzle involves armed career criminals and felons in possession of firearms, and they said the best approach is to put them behind bars and keep them there.

Federal firearms laws mostly carry harsher penalties than similar state statutes, and Satterberg said as long as that’s the case he will defer prosecuting those cases to Durkan’s office, where a special prosecutor reviews every firearms case to determine if it can be taken into the federal system.

“We cannot prosecute our way out of this problem,” Durkan said. “But we will prosecute those who are the problem.”

It’s not a new program — the feds have prosecuted selected gun crimes for nearly a decade under a Department of Justice program called “Weed and Seed.” Last year, 40 federal firearms cases were culled from about 200 cases reviewed. Durkan said she expects that number to increase under the new mandate.

Few people understand how lenient state gun-crime laws are, said Satterberg, who has pressed the Legislature for tougher penalties. Past efforts have failed.

Under state laws, a felon caught with a firearm might receive a two-year prison sentence, providing his underlying felony conviction is on a list of so-called “serious crimes,” mostly involving violence. If the underlying felony is not on the list of “serious crimes” — a theft or burglary, for example — as many as four gun-possession convictions are necessary before the offender might receive a one-year prison sentence.

Laws for juveniles are even more lax. Someone younger than 18 must be convicted of illegally possessing a firearm five times before receiving a 15-week sentence to a state juvenile-rehabilitation center.

By contract, a federal conviction of being a felon in possession of a firearm brings a possible 10-year prison sentence. Carrying a gun during a drug deal or another crime carries a mandatory five-year sentence, and felons caught with a gun who have three prior violent-crime or drug-related felony convictions face a mandatory 15-year federal prison term. Moreover, federal felons are supervised closely after release.

“The gun violence that has happened in our community is unacceptable,” said Seattle police Deputy Chief Nick Metz, who noted that since Jan. 1 police have recovered 361 guns, many of them stolen. During the same period, 81 guns have been reported stolen in Seattle, he said.

Monday’s announcement comes as the city grapples with a spike in homicides, mostly from gun violence. This year there have been 21 homicides in Seattle, one more than in all of last year. Nineteen of the deaths have resulted from gunfire.

On May 30, Ian Stawicki, a mentally ill 40-year-old, opened fire on patrons of Cafe Racer in Seattle’s University District, killing four and wounding one. Stawicki shot and killed a woman 30 minutes later as he carjacked her Mercedes-Benz SUV in a parking lot near downtown. He later shot himself in the head on a West Seattle sidewalk as police moved in to arrest him.

Two homicide victims this year were unintended targets of gunfire, police said. On May 24, Justin Ferrari was fatally shot while driving through the Central District. On April 22, Nicole Westbrook was hit by a stray bullet while walking home in Pioneer Square.

Over Memorial Day weekend, a bystander was shot in the calf near Seattle Center and members of an Asian street gang sprayed four houses with more than 60 bullets in a series of drive-by shootings in the Rainier Valley.